Subgroups — C₂×#28380675 #43243635

Order 28096.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊Dic₄₃₉	C₂	1	2	yes	maximal
2	#28380675	C₂	1	4	yes	maximal, direct product factor
3	C₂²×C₈×C₄₃₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×Dic₄₃₉	—	2	2	no	—
5	C₄⋊Dic₄₃₉	—	2	2	no	—
6	C₄⋊Dic₄₃₉	C₂²	1	4	yes	—
7	C₂²×C₄×C₄₃₉	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₄₃₉	C₄	1	4	yes	complemented
9	C₂×C₈×C₄₃₉	C₂²	1	2	yes	—
10	C₂×Dic₄₃₉	—	2	4	no	—
11	C₂×Dic₄₃₉	—	4	4	no	—
12	C₂³×C₄₃₉	D₄	1	1	yes	characteristic
13	C₂×C₄×C₄₃₉	C₂×C₄	1	2	yes	—
14	C₂×C₄×C₄₃₉	D₄	1	1	yes	characteristic
15	C₂×C₄×C₄₃₉	Q₈	1	2	yes	—
16	C₂×C₄×C₄₃₉	C₂³	1	1	yes	characteristic
17	C₈×C₄₃₉	C₂×C₄	1	4	yes	complemented
18	C₂²×C₄₃₉	C₄⋊C₄	1	2	yes	—
19	C₂²×C₄₃₉	SD₁₆	1	4	yes	—
20	C₂²×C₄₃₉	C₂×D₄	1	1	yes	characteristic
21	C₄×C₄₃₉	C₄⋊C₄	1	2	yes	—
22	C₄×C₄₃₉	C₂²×C₄	1	1	yes	characteristic
23	C₄×C₄₃₉	C₂×Q₈	1	1	yes	characteristic
24	Dic₄₃₉	—	4	4	no	—
25	C₂×C₄₃₉	#106	1	4	yes	complemented
26	C₂×C₄₃₉	C₂×C₄⋊C₄	1	1	yes	characteristic
27	C₂×C₄₃₉	C₂×SD₁₆	1	2	yes	—
28	C₄₃₉	C₂×#106	1	1	yes	characteristic, complemented, Sylow
29	C₂×#106	—	439	1	no	maximal, Sylow
30	C₂²×C₈	D₄₃₉	1	1	yes	characteristic
31	C₂×C₄⋊C₄	—	439	2	no	—
32	#106	—	439	4	no	—
33	C₂²×C₄	—	878	2	no	—
34	C₂²×C₄	C₂×D₄₃₉	1	1	yes	characteristic
35	C₂×C₈	Dic₄₃₉	1	4	yes	complemented
36	C₂×C₈	C₂×D₄₃₉	1	2	yes	—
37	C₄⋊C₄	—	878	2	no	—
38	C₄⋊C₄	—	439	4	no	—
39	C₂³	D₁₇₅₆	1	1	yes	characteristic
40	C₂×C₄	—	878	4	no	—
41	C₂×C₄	—	1756	4	no	—
42	C₂×C₄	C₂×Dic₄₃₉	1	2	yes	—
43	C₂×C₄	D₁₇₅₆	1	1	yes	characteristic
44	C₂×C₄	Dic₈₇₈	1	2	yes	—
45	C₂×C₄	C₂²×D₄₃₉	1	1	yes	characteristic
46	C₈	C₂×Dic₄₃₉	1	4	yes	complemented
47	C₂²	C₄⋊Dic₄₃₉	1	2	yes	—
48	C₂²	#20296318	1	4	yes	—
49	C₂²	C₂×D₁₇₅₆	1	1	yes	characteristic
50	C₄	—	1756	4	no	—
51	C₄	C₄⋊Dic₄₃₉	1	2	yes	—
52	C₄	C₂²×Dic₄₃₉	1	1	yes	characteristic
53	C₄	C₂×Dic₈₇₈	1	1	yes	characteristic
54	C₂	#28380675	1	4	yes	direct product factor
55	C₂	C₂×C₄⋊Dic₄₃₉	1	1	yes	characteristic
56	C₂	C₂×#20296318	1	2	yes	—

	subgroup	G/H
center	C₂³	D₁₇₅₆
commutator	C₄×C₄₃₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₄₃₉
Fitting	C₂²×C₈×C₄₃₉	C₂
socle, prime radical	C₂³×C₄₃₉	D₄
cosocle	C₂×C₄×C₄₃₉	C₂³
hypercenter	C₂²×C₈	D₄₃₉
hypocenter	C₄₃₉	C₂×#106
LCS	G ▷ C₄×C₄₃₉ ▷ C₂×C₄₃₉ ▷ C₄₃₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. #28380675	C₂	direct (N × H)
8. C₂×C₈×C₄₃₉	C₄	semidirect
17. C₈×C₄₃₉	C₂×C₄	semidirect
25. C₂×C₄₃₉	#106	semidirect
28. C₄₃₉	C₂×#106	semidirect
35. C₂×C₈	Dic₄₃₉	semidirect
46. C₈	C₂×Dic₄₃₉	semidirect
54. C₂	#28380675	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₄⋊Dic₄₃₉	2
#28380675	2
C₂²×C₈×C₄₃₉	2
C₂×#106	439

Subgroups — C2×#28380675 #43243635

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#28380675 #43243635